Hyperbolic Geometry
Poincaré disk, upper half-plane, and isometries of hyperbolic space.
Hyperbolic Geometry. Poincaré disk, upper half-plane, and isometries of hyperbolic space. This page collects canonical references that organise the subject and provide entry points to its main techniques.
Foundations and canonical references
The standard treatments of hyperbolic geometry approach the subject from complementary angles. Ratcliffe, Foundations of Hyperbolic Manifolds (2006) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.
Open methodological questions for hyperbolic geometry include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2006Foundations of Hyperbolic Manifoldsratcliffe-2006
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